Math Mondays::Be a Square!

Creative Math Club has started back up for those people in my area who also belong to the Out of the Box group on yahoo. The Math Club isn’t that old…we had it every week for 3 or 4 months in the springtime, and then stopped when summer appeared. I knew it was a success when my math phobic and totally math averse 12 year old asked if we could still do it on the weekends during summertime instead of stopping it altogether.

Creative Math is different from regular math in that it mixes art, music, and exploration with numbers and rules. Schools have stopped doing math this way because it takes a little longer to ‘discover’ math than it does to teach rote memorization for the NCLB standardized tests. It’s a shame.

This month, we’ve declared October to be Month of the Square. You know, square:

The younger kids tackled the actual shape concept, which I’ll cover another time. The older kids (4th grade and up) covered the exasperating concept (for me) of square numbers and square roots. And there were no tears! Or frustration! Or willful disobedience about it!

But first, the most important thing when hosting a math club for math averse, creative and divergent thinkers is good food, so everyone brought along square food. And if it wasn’t exactly square, we still ate it but just discussed why it wasn’t a square. We had chocolate squares, graham cracker squares, cheese cut into squares, square crackers, etc. etc.

The older kids sat at a table with a variety of square materials. First, they played around with square mosaic tiles (found at any craft store). This was done without any math discussion at all…just pure creative play.

After 15 minutes or so of mosaic patterning, correlating math patterns were brought up. In the example above there are a myriad of corresponding math facts. The kids were able to pattern it out without much prodding, for instance, if you look at the colors you start with:
1 black
3 white
5 red
7 black

One kid mentioned this, another kid noticed they were odd numbers, yet another predicted the next number would be 9, then 11, then, 13… Sonja, who was leading the older kids table, asked if they noticed what kind of number you got from adding two odd numbers together, odd or even.

Then, someone else notice that:

You may notice the square number pattern happening, but the kids didn’t, so we left their observations out there to linger until they were familiar with the actual square numbers. Some did notice, however, that the pattern was take the answer from the last equation and then add it to the next odd number in sequence. This interplay lasted another 15 minutes.

Next, the tiles were put away and some paper squares were brought out. Let the mosaics begin!

Free play with the paper squares took another 15 minutes, and then Sonja started directing their focus a little bit by asking, “How many squares do I need to make the smallest square?” The kids looked around and picked up 1 square paper….1. “This is the smallest square number. Number 1, and it is a square. What is the next smallest number that makes a square?” The kids looked around, played a bit with the papers, and set four of them together. “4” “4 is a square number, it’s not just a quantity, but also can be a shape…the shape of a square! Numbers that can form a square when you put them together in a grid are called Square numbers. See how many square numbers you can form!”

Some kids were methodical when finding square numbers, like this little girl who ordered them sequentially on her paper:

Some kids layed out a 12 by 12 grid…just as sequential, but more compact. Similar to the tiled pattern up above, only this time they had a correlation between the number patterns and the significance of them to ‘square numbers’.

And then some, as you notice in the background of the pic, used their papers to make happy faces. Since this is a freeform type of group, I really try hard not to mind if a kid isn’t necessarily sticking to the plan. Turns out, the happy face kid (who happens to be the Golfer) didn’t need to see or make the squares to know the square number pattern. He is more mathmatically minded and once he realized a square number was any number times itself he knew what the numbers were without referencing a visual square in his head. So, he made happy faces!

Naturalist made a mosaic that had a great deal of symmetry, and even mimicked two triangles forming a square:

We probably could have stopped there, but the kids were still happy around the table, and they had all grasped the concept of what a square number was by making square mosaics. So, Sonja introduced the idea of square roots. The usual diagram:

Only, when Sonja made the square root sign, for each line she said a word: The…Side…of the…Square…of number 4. Meaning, look at the square with 4 squares in it. How many squares are on the side? 2! That’s the square root, or side of the square. We practiced finding square roots in this manner until the kids grew restless. All told, they were at the table for 2 hours doing math and art at the same time…making mosaics and square numbers all at once!

And then, we ate square food like kings.

Math rocks!